Adjusting Historical Stock Returns for Dividends in VaR

Summary

The document considers how to include dividend income when estimating historical Value-at-Risk for a long stock position. Its proposed approach adjusts the return on the ex-dividend date by adding the dividend amount to the closing price before calculating the return relative to the prior price. This treats the dividend as cash received by the investor rather than as a loss in portfolio value when the share price falls to reflect the distribution.

The answer supports using dividend-adjusted arithmetic returns and clarifies that the adjustment belongs on the ex-dividend date, when the stock price reflects the dividend leaving the share, rather than on the later payment date. The discussion is conceptual and gives no empirical comparison of VaR estimates or treatment of reinvestment, taxes, or transaction costs. Its simple formula is framed for a single long position and historical return data.

Key ideas

• Dividend income should be included when measuring the return of a stock position for historical VaR.
• An arithmetic return can account for the distribution by adding the dividend to the ex-dividend price change.
• Apply the adjustment on the ex-dividend date rather than the cash payment date.
• The treatment described is a simple single-stock example and does not address taxes or reinvestment.

Tags

# Value-at-Risk and dividend payments


# Value-at-Risk and dividend payments












How should dividends be considered when computing Value-at-Risk for a stock portfolio using Historic data. To simplify let's consider a very simple portfolio of one long position on a stock. My VaR model setups is also very simple:

- I have returns for the stock for the past 500 days

- I then take the empircal distribution and call my 99% VaR as the 5th "worst" scenario

But how should I include the dividend payments for the stock? This question can be boiled down to: How should I take dividend payments into account and construct a new return series for the stock?

I have been considering to override the return at dividend payment days the following way:

$$\hat{r}_t=\frac{P_t+DVD-P_{t-1}}{P_{t-1}}$$ $\hat{r}_t$ is the new return. Are there any valid arguments that is is not a good way to tackle the problem mentioned above?

## Answer by byouness (score 1)

https://quant.stackexchange.com/a/39573

You are right, one should consider returns that are adjusted for dividends payments (if you go for arithmetic returns, then it's your $\hat{r}_t$).

The argument here is that this is the real return you get, because the dividend amount is detached from the stock, but is not lost (you get it in cash).

EDIT: To complete with Antoine's excellent comment, the adjustment should be made on the ex-dividend date rather than on he payment date.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.